Binomial Tree

Binomial Tree can compute either European and American option price.We can generalize the no-arbitrage argument just presented by considering a stock whose price is S0 and an option on the stock is f.

These are 1 and 5 steps binomial tree. Some of the parameters list below.

Let me compute European call option and American put option as a practice(R)

####Sample code####
##European Call###
europecall<-function(s0,k_call,vol,T,n,r)
{
  dt<-T/n
  u<-exp(vol*sqrt(dt))
  d<-exp(-vol*sqrt(dt))
  a<-exp(r*dt)
  p<-(a-d)/(u-d)
  strikeprice<-array(NA,c(n+1,n+1))
  strikeprice[1,1]<s0
  for(j in 2:(n+1))###j is step number
  {
    for(i in 1:j)###i is u step
    {
      stikeprice[i,j]<-s0*u^(j-2*i+1)
    }
  }
  ECV<-array(NA,c(n+1,n+1))
  for(i in 1:(n+1))
  {
    ECV[i,(n+1)]<-max(strikeprice[i,(n+1)]-k_call,0)
  }
  for(j in n:1)
  {
    for(i in 1:j)
    {
      ECV[i,j]<-(p*ECV[i,j+1]+(1-p)*ECV[i+1,j+1])*exp(-r*dt)  
    }
  }
  return(ECV[1,1])
}

##American Put##
apbt<-function(s0,k_put,vol,T,n,r)
{
dt<-T/n
u<-exp(vol*sqrt(dt))  
d<- exp(-vol*sqrt(dt))  
a<-exp(r*dt)    
p<-(a-d)/(u-d)    
STKP<-array(NA,c(n+1,n+1))    
STKP[1,1]<-s0
for(j in 2:(n+1))    
{
    for(i in 1:j)
    {
    STKP[i,j]<-s0*u^(j-2*i+1)    
}
}
APV<-array(NA,c(n+1,n+1))    
for(i in 1:(n+1))
{
    APV[i,n+1]<-max(k_put-STKP[i,n+1],0)    
}
for(j in n:1)
{
    for(i in 1:j)
    {
    epv<-(p*APV[i,j+1]+(1-p)*APV[i+1,j+1])*exp(-r*dt)    
APV[i,j]<-max(k_put-STKP[i,j],epv)     #choose whether to exercise the option earlier
}
}
return(APV[1,1])  
}

##Something I need to mention, I build this j steps binomial tree in a half upper matrix. The final column is a geometric progression, q=1/u^2###